Question: The equation of a circle $C$ is $x^2+y^2+10x-10y+25 = 0$. What is its center $(h, k)$ and its radius $r$ ?
Explanation: To find the equation in standard form, complete the square. $(x^2+10x) + (y^2-10y) = -25$ $(x^2+10x+25) + (y^2-10y+25) = -25 + 25 + 25$ $(x+5)^{2} + (y-5)^{2} = 25 = 5^2$ Thus, $(h, k) = (-5, 5)$ and $r = 5$.